Square matrix/Trace/Definition

Trace

Let ${}K$ be a field and let ${}M={\left(a_{ij}\right)}_{ij}$ be an ${}n\times n$-matrix over ${}K$. Then

${}\operatorname {trace} {\left(M\right)}:=\sum _{i=1}^{n}a_{ii}\,$

is called the trace of ${}M$.